convertPathData.js

'use strict';

exports.type = 'perItem';

exports.active = true;

exports.description = 'optimizes path data: writes in shorter form, applies transformations';

exports.params = {
    applyTransforms: true,
    applyTransformsStroked: true,
    makeArcs: {
        threshold: 2.5, // coefficient of rounding error
        tolerance: 0.5  // percentage of radius
    },
    straightCurves: true,
    lineShorthands: true,
    curveSmoothShorthands: true,
    floatPrecision: 3,
    transformPrecision: 5,
    removeUseless: true,
    collapseRepeated: true,
    utilizeAbsolute: true,
    leadingZero: true,
    negativeExtraSpace: true,
    noSpaceAfterFlags: true,
    forceAbsolutePath: false
};

var pathElems = require('./_collections.js').pathElems,
    path2js = require('./_path.js').path2js,
    js2path = require('./_path.js').js2path,
    applyTransforms = require('./_path.js').applyTransforms,
    cleanupOutData = require('../lib/svgo/tools').cleanupOutData,
    roundData,
    precision,
    error,
    arcThreshold,
    arcTolerance,
    hasMarkerMid,
    hasStrokeLinecap;

/**
 * Convert absolute Path to relative,
 * collapse repeated instructions,
 * detect and convert Lineto shorthands,
 * remove useless instructions like "l0,0",
 * trim useless delimiters and leading zeros,
 * decrease accuracy of floating-point numbers.
 *
 * @see http://www.w3.org/TR/SVG/paths.html#PathData
 *
 * @param {Object} item current iteration item
 * @param {Object} params plugin params
 * @return {Boolean} if false, item will be filtered out
 *
 * @author Kir Belevich
 */
exports.fn = function(item, params) {

    if (item.isElem(pathElems) && item.hasAttr('d')) {

        precision = params.floatPrecision;
        error = precision !== false ? +Math.pow(.1, precision).toFixed(precision) : 1e-2;
        roundData = precision > 0 && precision < 20 ? strongRound : round;
        if (params.makeArcs) {
            arcThreshold = params.makeArcs.threshold;
            arcTolerance = params.makeArcs.tolerance;
        }
        hasMarkerMid = item.hasAttr('marker-mid');

        var stroke = item.computedAttr('stroke'),
            strokeLinecap = item.computedAttr('stroke');
        hasStrokeLinecap = stroke && stroke != 'none' && strokeLinecap && strokeLinecap != 'butt';

        var data = path2js(item);

        // TODO: get rid of functions returns
        if (data.length) {
            convertToRelative(data);

            if (params.applyTransforms) {
                data = applyTransforms(item, data, params);
            }

            data = filters(data, params);

            if (params.utilizeAbsolute) {
                data = convertToMixed(data, params);
            }

            js2path(item, data, params);
        }

    }

};

/**
 * Convert absolute path data coordinates to relative.
 *
 * @param {Array} path input path data
 * @param {Object} params plugin params
 * @return {Array} output path data
 */
function convertToRelative(path) {

    var point = [0, 0],
        subpathPoint = [0, 0],
        baseItem;

    path.forEach(function(item, index) {

        var instruction = item.instruction,
            data = item.data;

        // data !== !z
        if (data) {

            // already relative
            // recalculate current point
            if ('mcslqta'.indexOf(instruction) > -1) {

                point[0] += data[data.length - 2];
                point[1] += data[data.length - 1];

                if (instruction === 'm') {
                    subpathPoint[0] = point[0];
                    subpathPoint[1] = point[1];
                    baseItem = item;
                }

            } else if (instruction === 'h') {

                point[0] += data[0];

            } else if (instruction === 'v') {

                point[1] += data[0];

            }

            // convert absolute path data coordinates to relative
            // if "M" was not transformed from "m"
            // M → m
            if (instruction === 'M') {

                if (index > 0) instruction = 'm';

                data[0] -= point[0];
                data[1] -= point[1];

                subpathPoint[0] = point[0] += data[0];
                subpathPoint[1] = point[1] += data[1];

                baseItem = item;

            }

            // L → l
            // T → t
            else if ('LT'.indexOf(instruction) > -1) {

                instruction = instruction.toLowerCase();

                // x y
                // 0 1
                data[0] -= point[0];
                data[1] -= point[1];

                point[0] += data[0];
                point[1] += data[1];

            // C → c
            } else if (instruction === 'C') {

                instruction = 'c';

                // x1 y1 x2 y2 x y
                // 0  1  2  3  4 5
                data[0] -= point[0];
                data[1] -= point[1];
                data[2] -= point[0];
                data[3] -= point[1];
                data[4] -= point[0];
                data[5] -= point[1];

                point[0] += data[4];
                point[1] += data[5];

            // S → s
            // Q → q
            } else if ('SQ'.indexOf(instruction) > -1) {

                instruction = instruction.toLowerCase();

                // x1 y1 x y
                // 0  1  2 3
                data[0] -= point[0];
                data[1] -= point[1];
                data[2] -= point[0];
                data[3] -= point[1];

                point[0] += data[2];
                point[1] += data[3];

            // A → a
            } else if (instruction === 'A') {

                instruction = 'a';

                // rx ry x-axis-rotation large-arc-flag sweep-flag x y
                // 0  1  2               3              4          5 6
                data[5] -= point[0];
                data[6] -= point[1];

                point[0] += data[5];
                point[1] += data[6];

            // H → h
            } else if (instruction === 'H') {

                instruction = 'h';

                data[0] -= point[0];

                point[0] += data[0];

            // V → v
            } else if (instruction === 'V') {

                instruction = 'v';

                data[0] -= point[1];

                point[1] += data[0];

            }

            item.instruction = instruction;
            item.data = data;

            // store absolute coordinates for later use
            item.coords = point.slice(-2);

        }

        // !data === z, reset current point
        else if (instruction == 'z') {
            if (baseItem) {
                item.coords = baseItem.coords;
            }
            point[0] = subpathPoint[0];
            point[1] = subpathPoint[1];
        }

        item.base = index > 0 ? path[index - 1].coords : [0, 0];

    });

    return path;

}

/**
 * Main filters loop.
 *
 * @param {Array} path input path data
 * @param {Object} params plugin params
 * @return {Array} output path data
 */
function filters(path, params) {

    var stringify = data2Path.bind(null, params),
        relSubpoint = [0, 0],
        pathBase = [0, 0],
        prev = {};

    path = path.filter(function(item, index, path) {

        var instruction = item.instruction,
            data = item.data,
            next = path[index + 1];

        if (data) {

            var sdata = data,
                circle;

            if (instruction === 's') {
                sdata = [0, 0].concat(data);

                if ('cs'.indexOf(prev.instruction) > -1) {
                    var pdata = prev.data,
                        n = pdata.length;

                    // (-x, -y) of the prev tangent point relative to the current point
                    sdata[0] = pdata[n - 2] - pdata[n - 4];
                    sdata[1] = pdata[n - 1] - pdata[n - 3];
                }

            }

            // convert curves to arcs if possible
            if (
                params.makeArcs &&
                (instruction == 'c' || instruction == 's') &&
                isConvex(sdata) &&
                (circle = findCircle(sdata))
            ) {
                var r = roundData([circle.radius])[0],
                    angle = findArcAngle(sdata, circle),
                    sweep = sdata[5] * sdata[0] - sdata[4] * sdata[1] > 0 ? 1 : 0,
                    arc = {
                        instruction: 'a',
                        data: [r, r, 0, 0, sweep, sdata[4], sdata[5]],
                        coords: item.coords.slice(),
                        base: item.base
                    },
                    output = [arc],
                    // relative coordinates to adjust the found circle
                    relCenter = [circle.center[0] - sdata[4], circle.center[1] - sdata[5]],
                    relCircle = { center: relCenter, radius: circle.radius },
                    arcCurves = [item],
                    hasPrev = 0,
                    suffix = '',
                    nextLonghand;

                if (
                    prev.instruction == 'c' && isConvex(prev.data) && isArcPrev(prev.data, circle) ||
                    prev.instruction == 'a' && prev.sdata && isArcPrev(prev.sdata, circle)
                ) {
                    arcCurves.unshift(prev);
                    arc.base = prev.base;
                    arc.data[5] = arc.coords[0] - arc.base[0];
                    arc.data[6] = arc.coords[1] - arc.base[1];
                    var prevData = prev.instruction == 'a' ? prev.sdata : prev.data;
                    var prevAngle = findArcAngle(prevData,
                        {
                            center: [prevData[4] + circle.center[0], prevData[5] + circle.center[1]],
                            radius: circle.radius
                        }
                    );
                    angle += prevAngle;
                    if (angle > Math.PI) arc.data[3] = 1;
                    hasPrev = 1;
                }

                // check if next curves are fitting the arc
                for (var j = index; (next = path[++j]) && ~'cs'.indexOf(next.instruction);) {
                    var nextData = next.data;
                    if (next.instruction == 's') {
                        nextLonghand = makeLonghand({instruction: 's', data: next.data.slice() },
                            path[j - 1].data);
                        nextData = nextLonghand.data;
                        nextLonghand.data = nextData.slice(0, 2);
                        suffix = stringify([nextLonghand]);
                    }
                    if (isConvex(nextData) && isArc(nextData, relCircle)) {
                        angle += findArcAngle(nextData, relCircle);
                        if (angle - 2 * Math.PI > 1e-3) break; // more than 360°
                        if (angle > Math.PI) arc.data[3] = 1;
                        arcCurves.push(next);
                        if (2 * Math.PI - angle > 1e-3) { // less than 360°
                            arc.coords = next.coords;
                            arc.data[5] = arc.coords[0] - arc.base[0];
                            arc.data[6] = arc.coords[1] - arc.base[1];
                        } else {
                            // full circle, make a half-circle arc and add a second one
                            arc.data[5] = 2 * (relCircle.center[0] - nextData[4]);
                            arc.data[6] = 2 * (relCircle.center[1] - nextData[5]);
                            arc.coords = [arc.base[0] + arc.data[5], arc.base[1] + arc.data[6]];
                            arc = {
                                instruction: 'a',
                                data: [r, r, 0, 0, sweep,
                                    next.coords[0] - arc.coords[0], next.coords[1] - arc.coords[1]],
                                coords: next.coords,
                                base: arc.coords
                            };
                            output.push(arc);
                            j++;
                            break;
                        }
                        relCenter[0] -= nextData[4];
                        relCenter[1] -= nextData[5];
                    } else break;
                }

                if ((stringify(output) + suffix).length < stringify(arcCurves).length) {
                    if (path[j] && path[j].instruction == 's') {
                        makeLonghand(path[j], path[j - 1].data);
                    }
                    if (hasPrev) {
                        var prevArc = output.shift();
                        roundData(prevArc.data);
                        relSubpoint[0] += prevArc.data[5] - prev.data[prev.data.length - 2];
                        relSubpoint[1] += prevArc.data[6] - prev.data[prev.data.length - 1];
                        prev.instruction = 'a';
                        prev.data = prevArc.data;
                        item.base = prev.coords = prevArc.coords;
                    }
                    arc = output.shift();
                    if (arcCurves.length == 1) {
                        item.sdata = sdata.slice(); // preserve curve data for future checks
                    } else if (arcCurves.length - 1 - hasPrev > 0) {
                        // filter out consumed next items
                        path.splice.apply(path, [index + 1, arcCurves.length - 1 - hasPrev].concat(output));
                    }
                    if (!arc) return false;
                    instruction = 'a';
                    data = arc.data;
                    item.coords = arc.coords;
                }
            }

            // Rounding relative coordinates, taking in account accummulating error
            // to get closer to absolute coordinates. Sum of rounded value remains same:
            // l .25 3 .25 2 .25 3 .25 2 -> l .3 3 .2 2 .3 3 .2 2
            if (precision !== false) {
                if ('mltqsc'.indexOf(instruction) > -1) {
                    for (var i = data.length; i--;) {
                        data[i] += item.base[i % 2] - relSubpoint[i % 2];
                    }
                } else if (instruction == 'h') {
                    data[0] += item.base[0] - relSubpoint[0];
                } else if (instruction == 'v') {
                    data[0] += item.base[1] - relSubpoint[1];
                } else if (instruction == 'a') {
                    data[5] += item.base[0] - relSubpoint[0];
                    data[6] += item.base[1] - relSubpoint[1];
                }
                roundData(data);

                if      (instruction == 'h') relSubpoint[0] += data[0];
                else if (instruction == 'v') relSubpoint[1] += data[0];
                else {
                    relSubpoint[0] += data[data.length - 2];
                    relSubpoint[1] += data[data.length - 1];
                }
                roundData(relSubpoint);

                if (instruction.toLowerCase() == 'm') {
                    pathBase[0] = relSubpoint[0];
                    pathBase[1] = relSubpoint[1];
                }
            }

            // convert straight curves into lines segments
            if (params.straightCurves) {

                if (
                    instruction === 'c' &&
                    isCurveStraightLine(data) ||
                    instruction === 's' &&
                    isCurveStraightLine(sdata)
                ) {
                    if (next && next.instruction == 's')
                        makeLonghand(next, data); // fix up next curve
                    instruction = 'l';
                    data = data.slice(-2);
                }

                else if (
                    instruction === 'q' &&
                    isCurveStraightLine(data)
                ) {
                    if (next && next.instruction == 't')
                        makeLonghand(next, data); // fix up next curve
                    instruction = 'l';
                    data = data.slice(-2);
                }

                else if (
                    instruction === 't' &&
                    prev.instruction !== 'q' &&
                    prev.instruction !== 't'
                ) {
                    instruction = 'l';
                    data = data.slice(-2);
                }

                else if (
                    instruction === 'a' &&
                    (data[0] === 0 || data[1] === 0)
                ) {
                    instruction = 'l';
                    data = data.slice(-2);
                }
            }

            // horizontal and vertical line shorthands
            // l 50 0 → h 50
            // l 0 50 → v 50
            if (
                params.lineShorthands &&
                instruction === 'l'
            ) {
                if (data[1] === 0) {
                    instruction = 'h';
                    data.pop();
                } else if (data[0] === 0) {
                    instruction = 'v';
                    data.shift();
                }
            }

            // collapse repeated commands
            // h 20 h 30 -> h 50
            if (
                params.collapseRepeated &&
                !hasMarkerMid &&
                ('mhv'.indexOf(instruction) > -1) &&
                prev.instruction &&
                instruction == prev.instruction.toLowerCase() &&
                (
                    (instruction != 'h' && instruction != 'v') ||
                    (prev.data[0] >= 0) == (item.data[0] >= 0)
            )) {
                prev.data[0] += data[0];
                if (instruction != 'h' && instruction != 'v') {
                    prev.data[1] += data[1];
                }
                prev.coords = item.coords;
                path[index] = prev;
                return false;
            }

            // convert curves into smooth shorthands
            if (params.curveSmoothShorthands && prev.instruction) {

                // curveto
                if (instruction === 'c') {

                    // c + c → c + s
                    if (
                        prev.instruction === 'c' &&
                        data[0] === -(prev.data[2] - prev.data[4]) &&
                        data[1] === -(prev.data[3] - prev.data[5])
                    ) {
                        instruction = 's';
                        data = data.slice(2);
                    }

                    // s + c → s + s
                    else if (
                        prev.instruction === 's' &&
                        data[0] === -(prev.data[0] - prev.data[2]) &&
                        data[1] === -(prev.data[1] - prev.data[3])
                    ) {
                        instruction = 's';
                        data = data.slice(2);
                    }

                    // [^cs] + c → [^cs] + s
                    else if (
                        'cs'.indexOf(prev.instruction) === -1 &&
                        data[0] === 0 &&
                        data[1] === 0
                    ) {
                        instruction = 's';
                        data = data.slice(2);
                    }

                }

                // quadratic Bézier curveto
                else if (instruction === 'q') {

                    // q + q → q + t
                    if (
                        prev.instruction === 'q' &&
                        data[0] === (prev.data[2] - prev.data[0]) &&
                        data[1] === (prev.data[3] - prev.data[1])
                    ) {
                        instruction = 't';
                        data = data.slice(2);
                    }

                    // t + q → t + t
                    else if (
                        prev.instruction === 't' &&
                        data[2] === prev.data[0] &&
                        data[3] === prev.data[1]
                    ) {
                        instruction = 't';
                        data = data.slice(2);
                    }

                }

            }

            // remove useless non-first path segments
            if (params.removeUseless && !hasStrokeLinecap) {

                // l 0,0 / h 0 / v 0 / q 0,0 0,0 / t 0,0 / c 0,0 0,0 0,0 / s 0,0 0,0
                if (
                    (
                     'lhvqtcs'.indexOf(instruction) > -1
                    ) &&
                    data.every(function(i) { return i === 0; })
                ) {
                    path[index] = prev;
                    return false;
                }

                // a 25,25 -30 0,1 0,0
                if (
                    instruction === 'a' &&
                    data[5] === 0 &&
                    data[6] === 0
                ) {
                    path[index] = prev;
                    return false;
                }

            }

            item.instruction = instruction;
            item.data = data;

            prev = item;

        } else {

            // z resets coordinates
            relSubpoint[0] = pathBase[0];
            relSubpoint[1] = pathBase[1];
            if (prev.instruction == 'z') return false;
            prev = item;

        }

        return true;

    });

    return path;

}

/**
 * Writes data in shortest form using absolute or relative coordinates.
 *
 * @param {Array} data input path data
 * @return {Boolean} output
 */
function convertToMixed(path, params) {

    var prev = path[0];

    path = path.filter(function(item, index) {

        if (index == 0) return true;
        if (!item.data) {
            prev = item;
            return true;
        }

        var instruction = item.instruction,
            data = item.data,
            adata = data && data.slice(0);

        if ('mltqsc'.indexOf(instruction) > -1) {
            for (var i = adata.length; i--;) {
                adata[i] += item.base[i % 2];
            }
        } else if (instruction == 'h') {
                adata[0] += item.base[0];
        } else if (instruction == 'v') {
                adata[0] += item.base[1];
        } else if (instruction == 'a') {
                adata[5] += item.base[0];
                adata[6] += item.base[1];
        }

        roundData(adata);

        var absoluteDataStr = cleanupOutData(adata, params),
            relativeDataStr = cleanupOutData(data, params);

        // Convert to absolute coordinates if it's shorter or forceAbsolutePath is true.
        // v-20 -> V0
        // Don't convert if it fits following previous instruction.
        // l20 30-10-50 instead of l20 30L20 30
        if (
            params.forceAbsolutePath || (
            absoluteDataStr.length < relativeDataStr.length &&
            !(
                params.negativeExtraSpace &&
                instruction == prev.instruction &&
                prev.instruction.charCodeAt(0) > 96 &&
                absoluteDataStr.length == relativeDataStr.length - 1 &&
                (data[0] < 0 || /^0\./.test(data[0]) && prev.data[prev.data.length - 1] % 1)
            ))
        ) {
            item.instruction = instruction.toUpperCase();
            item.data = adata;
        }

        prev = item;

        return true;

    });

    return path;

}

/**
 * Checks if curve is convex. Control points of such a curve must form
 * a convex quadrilateral with diagonals crosspoint inside of it.
 *
 * @param {Array} data input path data
 * @return {Boolean} output
 */
function isConvex(data) {

    var center = getIntersection([0, 0, data[2], data[3], data[0], data[1], data[4], data[5]]);

    return center &&
        (data[2] < center[0] == center[0] < 0) &&
        (data[3] < center[1] == center[1] < 0) &&
        (data[4] < center[0] == center[0] < data[0]) &&
        (data[5] < center[1] == center[1] < data[1]);

}

/**
 * Computes lines equations by two points and returns their intersection point.
 *
 * @param {Array} coords 8 numbers for 4 pairs of coordinates (x,y)
 * @return {Array|undefined} output coordinate of lines' crosspoint
 */
function getIntersection(coords) {

        // Prev line equation parameters.
    var a1 = coords[1] - coords[3], // y1 - y2
        b1 = coords[2] - coords[0], // x2 - x1
        c1 = coords[0] * coords[3] - coords[2] * coords[1], // x1 * y2 - x2 * y1

        // Next line equation parameters
        a2 = coords[5] - coords[7], // y1 - y2
        b2 = coords[6] - coords[4], // x2 - x1
        c2 = coords[4] * coords[7] - coords[5] * coords[6], // x1 * y2 - x2 * y1
        denom = (a1 * b2 - a2 * b1);

    if (!denom) return; // parallel lines havn't an intersection

    var cross = [
            (b1 * c2 - b2 * c1) / denom,
            (a1 * c2 - a2 * c1) / -denom
        ];
    if (
        !isNaN(cross[0]) && !isNaN(cross[1]) &&
        isFinite(cross[0]) && isFinite(cross[1])
    ) {
        return cross;
    }

}

/**
 * Decrease accuracy of floating-point numbers
 * in path data keeping a specified number of decimals.
 * Smart rounds values like 2.3491 to 2.35 instead of 2.349.
 * Doesn't apply "smartness" if the number precision fits already.
 *
 * @param {Array} data input data array
 * @return {Array} output data array
 */
function strongRound(data) {
    for (var i = data.length; i-- > 0;) {
        if (data[i].toFixed(precision) != data[i]) {
            var rounded = +data[i].toFixed(precision - 1);
            data[i] = +Math.abs(rounded - data[i]).toFixed(precision + 1) >= error ?
                +data[i].toFixed(precision) :
                rounded;
        }
    }
    return data;
}

/**
 * Simple rounding function if precision is 0.
 *
 * @param {Array} data input data array
 * @return {Array} output data array
 */
function round(data) {
    for (var i = data.length; i-- > 0;) {
        data[i] = Math.round(data[i]);
    }
    return data;
}

/**
 * Checks if a curve is a straight line by measuring distance
 * from middle points to the line formed by end points.
 *
 * @param {Array} xs array of curve points x-coordinates
 * @param {Array} ys array of curve points y-coordinates
 * @return {Boolean}
 */

function isCurveStraightLine(data) {

    // Get line equation a·x + b·y + c = 0 coefficients a, b (c = 0) by start and end points.
    var i = data.length - 2,
        a = -data[i + 1], // y1 − y2 (y1 = 0)
        b = data[i],      // x2 − x1 (x1 = 0)
        d = 1 / (a * a + b * b); // same part for all points

    if (i <= 1 || !isFinite(d)) return false; // curve that ends at start point isn't the case

    // Distance from point (x0, y0) to the line is sqrt((c − a·x0 − b·y0)² / (a² + b²))
    while ((i -= 2) >= 0) {
        if (Math.sqrt(Math.pow(a * data[i] + b * data[i + 1], 2) * d) > error)
            return false;
    }

    return true;

}

/**
 * Converts next curve from shorthand to full form using the current curve data.
 *
 * @param {Object} item curve to convert
 * @param {Array} data current curve data
 */

function makeLonghand(item, data) {
    switch (item.instruction) {
        case 's': item.instruction = 'c'; break;
        case 't': item.instruction = 'q'; break;
    }
    item.data.unshift(data[data.length - 2] - data[data.length - 4], data[data.length - 1] - data[data.length - 3]);
    return item;
}

/**
 * Returns distance between two points
 *
 * @param {Array} point1 first point coordinates
 * @param {Array} point2 second point coordinates
 * @return {Number} distance
 */

function getDistance(point1, point2) {
    return Math.hypot(point1[0] - point2[0], point1[1] - point2[1]);
}

/**
 * Returns coordinates of the curve point corresponding to the certain t
 * a·(1 - t)³·p1 + b·(1 - t)²·t·p2 + c·(1 - t)·t²·p3 + d·t³·p4,
 * where pN are control points and p1 is zero due to relative coordinates.
 *
 * @param {Array} curve array of curve points coordinates
 * @param {Number} t parametric position from 0 to 1
 * @return {Array} Point coordinates
 */

function getCubicBezierPoint(curve, t) {
    var sqrT = t * t,
        cubT = sqrT * t,
        mt = 1 - t,
        sqrMt = mt * mt;

    return [
        3 * sqrMt * t * curve[0] + 3 * mt * sqrT * curve[2] + cubT * curve[4],
        3 * sqrMt * t * curve[1] + 3 * mt * sqrT * curve[3] + cubT * curve[5]
    ];
}

/**
 * Finds circle by 3 points of the curve and checks if the curve fits the found circle.
 *
 * @param {Array} curve
 * @return {Object|undefined} circle
 */

function findCircle(curve) {
    var midPoint = getCubicBezierPoint(curve, 1/2),
        m1 = [midPoint[0] / 2, midPoint[1] / 2],
        m2 = [(midPoint[0] + curve[4]) / 2, (midPoint[1] + curve[5]) / 2],
        center = getIntersection([
            m1[0], m1[1],
            m1[0] + m1[1], m1[1] - m1[0],
            m2[0], m2[1],
            m2[0] + (m2[1] - midPoint[1]), m2[1] - (m2[0] - midPoint[0])
        ]),
        radius = center && getDistance([0, 0], center),
        tolerance = Math.min(arcThreshold * error, arcTolerance * radius / 100);

    if (center && radius < 1e15 &&
        [1/4, 3/4].every(function(point) {
        return Math.abs(getDistance(getCubicBezierPoint(curve, point), center) - radius) <= tolerance;
    }))
        return { center: center, radius: radius};
}

/**
 * Checks if a curve fits the given circle.
 *
 * @param {Object} circle
 * @param {Array} curve
 * @return {Boolean}
 */

function isArc(curve, circle) {
    var tolerance = Math.min(arcThreshold * error, arcTolerance * circle.radius / 100);

    return [0, 1/4, 1/2, 3/4, 1].every(function(point) {
        return Math.abs(getDistance(getCubicBezierPoint(curve, point), circle.center) - circle.radius) <= tolerance;
    });
}

/**
 * Checks if a previous curve fits the given circle.
 *
 * @param {Object} circle
 * @param {Array} curve
 * @return {Boolean}
 */

function isArcPrev(curve, circle) {
    return isArc(curve, {
        center: [circle.center[0] + curve[4], circle.center[1] + curve[5]],
        radius: circle.radius
    });
}

/**
 * Finds angle of a curve fitting the given arc.

 * @param {Array} curve
 * @param {Object} relCircle
 * @return {Number} angle
 */

function findArcAngle(curve, relCircle) {
    var x1 = -relCircle.center[0],
        y1 = -relCircle.center[1],
        x2 = curve[4] - relCircle.center[0],
        y2 = curve[5] - relCircle.center[1];

    return Math.acos(
            (x1 * x2 + y1 * y2) /
            Math.sqrt((x1 * x1 + y1 * y1) * (x2 * x2 + y2 * y2))
        );
}

/**
 * Converts given path data to string.
 *
 * @param {Object} params
 * @param {Array} pathData
 * @return {String}
 */

function data2Path(params, pathData) {
    return pathData.reduce(function(pathString, item) {
        var strData = '';
        if (item.data) {
            strData = cleanupOutData(roundData(item.data.slice()), params);
        }
        return pathString + item.instruction + strData;
    }, '');
}